A circle's center is at #(2 ,5 )# and it passes through #(1 ,4 )#. What is the length of an arc covering #( pi ) /3 # radians on the circle?

1 Answer
Leland Adriano Alejandro
Feb 17, 2016

length of arc#=(sqrt2*pi)/3=1.48096" "#units

Explanation:

To solve for the length of arc s:
Use the formula

#s=r*theta# using the given data: #theta=pi/3# and computed value of #r#

to compute for r: use distance formula with points center #(x_c, y_c)=(2, 5)# and the given point #(x_1, y_1)=(1, 4)#

#r=sqrt((x_c-x_1)^2+(y_c-y_1)^2)#

#r=sqrt((2-1)^2+(5-4)^2)#

#r=sqrt2#

Solve arc length #s#

#s=r*theta=sqrt2 *pi/3#

#s=(sqrt2*pi)/3=1.48096" "#units

God bless America !

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